Papers Published
Abstract:
The goal of this paper is to develop the theory of Deligne-Beilinson
cohomology of affine groups with a mixed Hodge structure. The motivation comes
from Hodge theory and the study of motives, where such groups appear. Several
of Francis Brown's period computations (arXiv:1407.5167) are interpreted as
elements of the DB cohomology of the relative unipotent completion of $SL_2(Z)$
and their cup products. The results in this paper are used in arXiv:1403.6443
where they are used to prove that Pollack's quadratic relations are motivic.